Use the model $A=P e^{r t}$ or $A=P\left(1+\frac{r}{n}\right)^{n t}$, where $A$ is the future value of $P$ dollars invested at interest rate $r$ compounded continuously or $n$ times per year for $t$ years.
A $\$ 5500$ bond grows to $\$ 7335.67$ in 6 years under continuous compounding. Find the interest rate. Round to the nearest whole percent.
Answer
Final Answer: The interest rate is \(\boxed{5\%}\).
Step 1 ：We are given a bond of $5500 that grows to $7335.67 in 6 years under continuous compounding. We need to find the interest rate.
Step 2 ：We can use the formula for continuous compounding, which is \(A=P e^{r t}\), where \(A\) is the future value, \(P\) is the principal, \(r\) is the interest rate, and \(t\) is the time in years.
Step 3 ：Substituting the given values into the formula, we get \(7335.67 = 5500 e^{r \times 6}\).
Step 4 ：Solving this equation for \(r\), we get \(r = 0.048000109676938706\).
Step 5 ：Rounding this to the nearest whole percent, we get \(r = 5\%\).
Step 6 ：Final Answer: The interest rate is \(\boxed{5\%}\).
